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100 tiles are labeled with the integers from 1 to 100 inclus
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30 Jul 2018, 11:00
30 Jul 2018, 11:00
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100 tiles are labeled with the integers from 1 to 100 inclusive; no numbers are repeated. If Alma chooses one tile at random, replaces it in the group, and chooses another tile at random, what is the probability that the product of the two integer values on the tiles is odd?
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{1}{2}\)
(E) \(\frac{3}{4}\)
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{1}{2}\)
(E) \(\frac{3}{4}\)
Re: 100 tiles are labeled with the integers from 1 to 100 inclus
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01 Aug 2018, 09:19
01 Aug 2018, 09:19
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Total number of tiles = 100
Numbering starts with odd and ends with even. i.e from 1 to 100. Therefore there are 50 odd tiles and 50 even tiles.
For product of two number to be odd, both number has to be odd.
Hence number of successful outcome = 50 * 50
Number of possible outcome = 100* 100
Probability = 50*50/100*100 = 1/4
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Numbering starts with odd and ends with even. i.e from 1 to 100. Therefore there are 50 odd tiles and 50 even tiles.
For product of two number to be odd, both number has to be odd.
Hence number of successful outcome = 50 * 50
Number of possible outcome = 100* 100
Probability = 50*50/100*100 = 1/4
Posted from my mobile device
Re: 100 tiles are labeled with the integers from 1 to 100 inclus
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09 Aug 2018, 14:44
09 Aug 2018, 14:44
Expert Reply
Explanation
Use both probability and number properties concepts in order to answer this question.
First, in order for two integers to produce an odd integer, the two starting integers must be odd. An odd times an odd equals an odd. An even times an odd, by contrast, produces an even, as does an even times an even.
Within the set of tiles, there are 50 even numbers (2, 4, 6, …, 100) and 50 odd numbers (1, 3, 5, …,99).
One randomly-chosen tile will have a \(\frac{50}{100}=\frac{1}{2}\) probability of being even, and a \(\frac{1}{2}\) probability of being odd.
The probability of choosing an odd tile first is \(\frac{1}{2}\) and the probability of choosing an odd tile second is also , so the probability of “first odd and second odd” is \(\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\).
Use both probability and number properties concepts in order to answer this question.
First, in order for two integers to produce an odd integer, the two starting integers must be odd. An odd times an odd equals an odd. An even times an odd, by contrast, produces an even, as does an even times an even.
Within the set of tiles, there are 50 even numbers (2, 4, 6, …, 100) and 50 odd numbers (1, 3, 5, …,99).
One randomly-chosen tile will have a \(\frac{50}{100}=\frac{1}{2}\) probability of being even, and a \(\frac{1}{2}\) probability of being odd.
The probability of choosing an odd tile first is \(\frac{1}{2}\) and the probability of choosing an odd tile second is also , so the probability of “first odd and second odd” is \(\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\).
